Calculate the quotient below and give your answer in scientific notation. ${\dfrac{1.64\times 10^{0}}{2.0\times 10^{2}}} =\ ?$
Start by collecting the significands and exponents. $ {\dfrac {{1.64} \times {10^{0}}} {{2.0} \times {10^{2}}} = {\dfrac{1.64}{2.0}} \times {\dfrac{10^{0}}{10^{2}}}} $ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= {0.82} \times {10^{0 \,-\, 2}}$ $= {0.82} \times {10^{-2}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the right without changing the value of our answer. We can use the fact that ${0.82}$ is the same as ${8.2 \div 10}$, or ${8.2 \times 10^{-1}}$. $ = {8.2 \times 10^{-1}} \times {10^{-2}} $ $ = 8.2 \times 10^{{-1} + {-2}} $ $= 8.2\times 10^{-3}$